scholarly journals Examples of Non-Semisimple Hopf Algebra Actions on Artin-Schelter Regular Algebras

2022 ◽  
Author(s):  
Hui-Xiang Chen ◽  
Ding-Guo Wang ◽  
James J. Zhang
Keyword(s):  
Hopf Algebra ◽  
Semisimple Hopf Algebra ◽  
Regular Algebras

scholarly journals The Jacobian, Reflection Arrangement and Discriminant for Reflection Hopf Algebras

2020 ◽  
Author(s):  
E Kirkman ◽  
J J Zhang
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Semisimple Hopf Algebra ◽  
Finite Dimensional ◽  
Regular Algebras ◽  
Noncommutative Setting ◽  
Reflection Arrangement

Abstract We study finite-dimensional semisimple Hopf algebra actions on noetherian connected graded Artin–Schelter regular algebras and introduce definitions of the Jacobian, the reflection arrangement, and the discriminant in a noncommutative setting.

scholarly journals Depth two Hopf subalgebras of a semisimple Hopf algebra

2009 ◽  
Vol 322 (1) ◽  
pp. 162-176 ◽  
Author(s):  
Sebastian Burciu ◽  
Lars Kadison
Keyword(s):  
Hopf Algebra ◽  
Semisimple Hopf Algebra

On Semisimple Hopf Algebras of Dimension pqn

2014 ◽  
Vol 57 (2) ◽  
pp. 264-269
Author(s):  
Li Dai ◽  
Jingcheng Dong
Keyword(s):  
Hopf Algebra ◽  
Group Algebra ◽  
Hopf Algebras ◽  
Prime Numbers ◽  
Closed Field ◽  
Semisimple Hopf Algebra ◽  
Algebraically Closed Field

AbstractLet p, q be prime numbers with p2 < q, n ∊ ℕ, and H a semisimple Hopf algebra of dimension pqn over an algebraically closed field of characteristic 0. This paper proves that H must possess one of the following two structures: (1) H is semisolvable; (2) H is a Radford biproduct R#kG, where kG is the group algebra of group G of order p and R is a semisimple Yetter–Drinfeld Hopf algebra in of dimension qn.

THE CALABI–YAU PROPERTY OF TWISTED SMASH PRODUCTS

2013 ◽  
Vol 13 (03) ◽  
pp. 1350118 ◽  
Author(s):  
DINGGUO WANG ◽  
YUANYUAN KE
Keyword(s):  
Hopf Algebra ◽  
Smash Product ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Semisimple Hopf Algebra ◽  
Finite Dimensional ◽  
Necessary And Sufficient

Let H be a finite-dimensional cocommutative semisimple Hopf algebra and A * H a twisted smash product. The Calabi–Yau (CY) property of twisted smash product is discussed. It is shown that if A is a CY algebra of dimension dA, a necessary and sufficient condition for A * H to be a CY Hopf algebra is given.

Kernels of representations of Drinfeld doubles of finite groups

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Sebastian Burciu
Keyword(s):  
Hopf Algebra ◽  
Finite Groups ◽  
Fusion Category ◽  
Semisimple Hopf Algebra ◽  
Normal Hopf Subalgebras

AbstractA description of the commutator of a normal subcategory of the fusion category of representation Rep A of a semisimple Hopf algebra A is given. Formulae for the kernels of representations of Drinfeld doubles D(G) of finite groups G are presented. It is shown that all these kernels are normal Hopf subalgebras.

scholarly journals Semisimple Hopf Algebras of Dimension 2q3

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Jingcheng Dong ◽  
Li Dai
Keyword(s):  
Hopf Algebra ◽  
Prime Number ◽  
Hopf Algebras ◽  
Closed Field ◽  
Semisimple Hopf Algebra ◽  
Algebraically Closed Field

AbstractLet q be a prime number, k an algebraically closed field of characteristic 0, and H a non-trivial semisimple Hopf algebra of dimension 2q

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